Gradient Texture Map to Ring Inset
If you are using Cycles render engine you could easily use a gradient texture as illustrated in the node setup bellow, though I am not sure it can be animated, as color ramp handles can't be keyframed as far as I know.

Has suggested by timaroberts, you can then animate this as desired by keyframing the position of the Color ramp handles in the Pos value.





Otherwise your best bet is probably unwrapping your mesh and animating the UV coordinates. You could then use a regular linear gradient with it.